Laser Operation and Bose-Einstein Condensation: Analogies and Differences

A. Chiocchetta; A. Gambassi; I. Carusotto

doi:10.1017/9781316084366.022

20 - Laser Operation and Bose-Einstein Condensation: Analogies and Differences

from Part IV - Condensates in Condensed Matter Physics

Published online by Cambridge University Press: 18 May 2017

A. Gambassi and

Edited by

David W. Snoke and

A. Chiocchetta: Affiliation:
SISSA - International School for Advanced Studies and INFN
A. Gambassi: Affiliation:
SISSA - International School for Advanced Studies and INFN
I. Carusotto: Affiliation:
INO-CNR BEC Center and Dipartimento di Fisica, Università di Trento,
Nick P. Proukakis: Affiliation:
Newcastle University
David W. Snoke: Affiliation:
University of Pittsburgh
Peter B. Littlewood: Affiliation:
University of Chicago

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Summary

After reviewing the interpretation of laser operation as a nonequilibrium Bose-Einstein condensation phase transition, we illustrate the novel features arising from the nonequilibrium nature of photon and polariton Bose-Einstein condensates recently observed in experiments. We then propose a quantitative criterion to experimentally assess the equilibrium versus nonequilibrium nature of a specific condensation process, based on fluctuation-dissipation relations. The power of this criterion is illustrated on two models which show very different behaviors.

Historical and Conceptual Introduction

The first introduction of concepts of nonequilibrium statistical mechanics into the realm of optics dates back to the early 1970s with pioneering works by Graham and Haken [1] and by DeGiorgio and Scully [2], who proposed a very insightful interpretation of the laser threshold in terms of a spontaneous breaking of the U(1) symmetry associated with the phase of the emitted light. Similar to what happens to the order parameter at a second-order phase transition, such an optical phase is randomly chosen every time the device is switched on and remains constant for macroscopic times. Moreover, a long-range spatial order is established, as light emitted by a laser device above threshold is phase-coherent on macroscopic distances.

While textbooks typically discuss this interpretation of laser operation in terms of a phase transition for the simplest case of a single-mode laser cavity, rigorously speaking this is valid only in spatially infinite systems. In fact, only in this case one can observe nonanalytic behaviors of the physical quantities at the transition point. In particular, the long-range order is typically assessed by looking at the long-distance behavior of the correlation function of the order parameter, which, for a laser, corresponds to the first-order spatial coherence of the emitted electric field,

the spontaneous symmetry breaking is signaled by this quantity becoming nonzero (see Chapter 5). The average is taken on the stationary density matrix of the system. In order to be able to probe this long-distance behavior, experimental studies need devices with a spatially extended active region.

Type: Chapter
Information: Universal Themes of Bose-Einstein Condensation , pp. 409 - 423

DOI: https://doi.org/10.1017/9781316084366.022 [Opens in a new window]

Publisher: Cambridge University Press

Print publication year: 2017

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References

[1] Graham, R., and Haken, H. 1970. Laserlight – first example of a second-order phase transition far away from thermal equilibrium. Z. Phys. A, 237, 31–46.Google Scholar

[2] DeGiorgio, V., and Scully, M. O. 1970. Analogy between the laser threshold region and a second-order phase transition. Phys. Rev. A, 2, 1170–1177.Google Scholar

[3] Chang-Hasnain, C. J. 2000. Tunable VCSEL. IEEE J. Sel. Top. Quantum Electron., 6(6), 978–987.Google Scholar

[4] Lundeberg, L. D. A., Lousberg, G. P., Boiko, D. L., and Kapon, E. 2007. Spatial coherence measurements in arrays of coupled vertical cavity surface emitting lasers. Appl. Phys. Lett., 90, 021103.Google Scholar

[5] Huang, K. 1987. Statistical Mechanics. Wiley.

[6] Pitaevskii, L. P., and Stringari, S. 2016. Bose-Einstein Condensation and Superfluidity. Oxford University Press.

[7] Penrose, O., and Onsager, L. 1956. Bose-Einstein condensation and liquid helium. Phys. Rev., 104, 576–584.Google Scholar

[8] Kasprzak, J., Richard, M., Kundermann, S., Baas, A., Jeambrun, P., Keeling, J. M. J., Marchetti, F. M., Szymanska, M. H., Andre, R., Staehli, J. L., Savona, V., Littlewood, P. B., Deveaud, B., and Dang, L. S. 2006. Bose-Einstein condensation of exciton polaritons. Nature, 443, 409–414.Google Scholar

[9] Demokritov, S. O., Demidov, V. E., Dzyapko, O., Melkov, G. A., Serga, A. A., Hillebrands, B., and Slavin, A. N. 2006. Bose–Einstein condensation of quasiequilibrium magnons at room temperature under pumping. Nature, 443, 430–433.Google Scholar

[10] Klaers, J., Schmitt, J., Vewinger, F., and Weitz, M. 2010. Bose-Einstein condensation of photons in an optical microcavity. Nature, 468, 545–548.Google Scholar

[11] Gunton, J. D., and Buckingham, M. J. 1968. Condensation of the ideal Bose gas as a cooperative transition. Phys. Rev., 166, 152–158.Google Scholar

[12] Castin, Y. 2001. Bose-Einstein condensates in atomic gases: simple theoretical results. Pages 1–136 of: Coherent Atomic Matter Waves. Springer.

[13] Castin, Y., and Dalibard, J. 1997. Relative phase of two Bose-Einstein condensates. Phys. Rev. A, 55, 4330–4337.Google Scholar

[14] Snoke, D. W., and Girvin, S. M. 2013. Dynamics of phase coherence onset in Bose condensates of photons by incoherent phonon emission. Journal of Low Temperature Physics, 171, 1–12.Google Scholar

[15] Lewenstein, M., and You, L. 1996. Quantum phase diffusion of a Bose-Einstein condensate. Phys. Rev. Lett., 77, 3489–3493.Google Scholar

[16] Carusotto, I., and Ciuti, C. 2013. Quantum fluids of light. Rev. Mod. Phys., 85, 299–366.Google Scholar

[17] Richard, M., Kasprzak, J., Romestain, R., André, R., and Dang, L. S. 2005. Spontaneous coherent phase transition of polaritons in CdTe microcavities. Phys. Rev. Lett., 94, 187401.Google Scholar

[18] Richard, M., Kasprzak, J., André, R., Romestain, R., Dang, L. S., Malpuech, G., and Kavokin, A. 2005. Experimental evidence for nonequilibrium Bose condensation of exciton polaritons. Phys. Rev. B, 72, 201301.Google Scholar

[19] Wouters, M., Carusotto, I., and Ciuti, C. 2008. Spatial and spectral shape of inhomogeneous nonequilibrium exciton-polariton condensates. Phys. Rev. B, 77, 115340.Google Scholar

[20] Wertz, E., Ferrier, L., Solnyshkov, D. D., Johne, R., Sanvitto, D., Lemaître, A., Sagnes, I., Grousson, R., Kavokin, A. V., Senellart, P., Malpuech, G., and Bloch, J. 2010. Spontaneous formation and optical manipulation of extended polariton condensates. Nat. Phys., 6, 860–864.Google Scholar

[21] Wouters, M., and Carusotto, I. 2006. Absence of long-range coherence in the parametric emission of photonic wires. Phys. Rev. B, 74, 245316.Google Scholar

[22] Wouters, M., and Carusotto, I. 2007. Goldstone mode of optical parametric oscillators in planar semiconductor microcavities in the strong-coupling regime. Phys. Rev. A, 76, 043807.Google Scholar

[23] Szymańska, M. H., Keeling, J., and Littlewood, P. B. 2006. Nonequilibrium quantum condensation in an incoherently pumped dissipative system. Phys. Rev. Lett., 96, 230602.Google Scholar

[24] Wouters, M., and Carusotto, I. 2007. Excitations in a nonequilibrium Bose-Einstein condensate of exciton polaritons. Phys. Rev. Lett., 99, 140402.Google Scholar

[25] Reatto, L., and Chester, G. V. 1967. Phonons and the properties of a Bose system. Phys. Rev., 155, 88–100.Google Scholar

[26] Popov, V. N. 1972. On the theory of the superfluidity of two- and one-dimensional Bose systems. Theor. Math. Phys., 11, 565–573.Google Scholar

[27] Sieberer, L. M., Huber, S. D., Altman, E., and Diehl, S. 2013. Dynamical critical phenomena in driven-dissipative systems. Phys. Rev. Lett., 110, 195301.Google Scholar

[28] Altman, E., Sieberer, L. M., Chen, L., Diehl, S., and Toner, J. 2015. Two-dimensional superfluidity of exciton polaritons requires strong anisotropy. Phys. Rev. X, 5, 011017.Google Scholar

[29] Bajoni, D., Senellart, P., Lemaître, A., and Bloch, J. 2007. Photon lasing in GaAs microcavity: similarities with a polariton condensate. Phys. Rev. B, 76, 201305.Google Scholar

[30] Fischer, B., and Weill, R. 2012. When does single-mode lasing become a condensation phenomenon? Opt. Express, 20, 26704–26713.

[31] Chiocchetta, A., and Carusotto, I. 2014. Quantum Langevin model for nonequilibrium condensation. Phys. Rev. A, 90, 023633.Google Scholar

[32] Kubo, R. 1966. The fluctuation-dissipation theorem. Rep. Prog. Phys., 29, 255.Google Scholar

[33] Mahan, G. D. 2000. Many-Particle Physics. Springer Science&Business Media.

[34] Kubo, R. 1957. Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn., 12, 570–586.Google Scholar

[35] Martin, P. C., and Schwinger, J. 1959. Theory of many-particle systems. I. Phys. Rev., 115, 1342–1373.Google Scholar

[36] Cugliandolo, L. F. 2011. The effective temperature. J. Phys. A: Math. Theor., 44, 483001.Google Scholar

[37] Foini, L., Cugliandolo, L. F., and Gambassi, A. 2011. Fluctuation-dissipation relations and critical quenches in the transverse field Ising chain. Phys. Rev. B, 84, 212404.Google Scholar

[38] Foini, L., Cugliandolo, L. F., and Gambassi, A. 2012. Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain. J. Stat. Mech., 2012, P09011.Google Scholar

[39] Walls, D. F., and Milburn, G. J. 2007. Quantum Optics. Springer Science&Business Media.

[40] Talkner, P. 1986. The failure of the quantum regression hypothesis. Annals of Physics, 167, 390–436.Google Scholar

[41] Ford, G. W., and O'Connell, R. F. 1996. There is no quantum regression theorem. Phys. Rev. Lett., 77, 798–801.Google Scholar

[42] Gardiner, C., and Zoller, P. 2004. Quantum Noise: A Handbook of Markovian and Non-Markovian Quantum Stochastic Methods with Applications to Quantum Optics. Vol. 56. Springer Science&Business Media.

[43] Kirton, P., and Keeling, J. 2013. Nonequilibrium model of photon condensation. Phys. Rev. Lett., 111, 100404.Google Scholar

[44] Kirton, P., and Keeling, J. 2015. Thermalization and breakdown of thermalization in photon condensates. Phys. Rev. A, 91, 033826.Google Scholar

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20 - Laser Operation and Bose-Einstein Condensation: Analogies and Differences

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